This paper gives a general formulation of convolutions for arbitrary linear operators from a linear space to a commutative algebra, constructs three convolutions for the Fourier transforms with geometric variables and four generalized convolutions for the Fourier-cosine, Fourier-sine transforms. With respect to applications, by using the constructed convolutions normed rings on L₁(Rⁿ) are constructed, and explicit solutions of integral equations of convolution type are obtained. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Giang B.T., Mau N.V., Tuan N.M.

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